Mean Shift Paper by Comaniciu and Meer Presentation by Carlo Lopez-Tello What Is the Mean Shift Algorithm?

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Mean Shift Paper by Comaniciu and Meer Presentation by Carlo Lopez-Tello What is the Mean Shift Algorithm? ● A method of finding peaks (modes) in a probability distribution ● Works without assuming any underlying structure in the distribution ● Works on multimodal distributions ● Works without assuming the number of modes Why do we care about modes? ● Given a data set we can assume that it was sampled from some pdf ● Samples are most likely to be drawn from a region near a mode ● We can use the modes to cluster the data ● Clustering has many applications: filtering, segmentation, tracking, classification, and compression. Why do we care about modes? Why use mean shift for clustering? ● K-means needs to know how many clusters to use. Clusters data into voronoi cells. ● Histograms require bin size and number of bins ● Mixture models require information about pdf structure Intuition ● We have a set of data that represents discrete samples of a distribution ● Locally we can estimate the density of the distribution with a function ● Compute the gradient of this estimation function ● Use gradient ascent to find the peak of the distribution How does it work? ● We estimate the density using: ● Where h (bandwidth) is the region around x where we are trying to estimate the density and k is some kernel function ● Instead of using the gradient of f, we use the mean shift vector: How to find a mode? 1. Start at any point 2. Compute mean shift 3. if mean shift is zero: possible mode found 4. else move to where mean shift is pointing go to 2 ● To find multiple modes we need to try all points that are more than h distance apart ● Prune modes by perturbing them and checking for convergence ● Combine modes that are close together. Take the higher one. How to cluster using mean shift? ● Every point in the data set will converge to some mode using mean shift ● We cluster points together if they converge to the same mode Mean Shift Filtering ● Cluster using intensity and position. Then change the intensity to match the cluster. Mean Shift Segmentation ● Cluster using intensity and spatial information. Each cluster represents a segment of the image. Discussion ● Need to select bandwidth and kernel function ● Gaussian kernel performs better, but takes longer to converge ● Kernel density estimation does not scale well with the dimension of the space. Questions.

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